Tiêu đề WK4 - Y5 - MATH - HW - COMBINATION & PERMUTATION - AN.docx.pdf ✅

Question 1: Step 1: Total paintings Leonardo Da Vinci has = 6 There are 6 options to choose 1st painting, 5 options to choose 2nd painting, 4 options to choose 3rd painting. Step 2: Number of ways 3 paintings can be chosen from 6 is = 6 * 5 * 4 = 120 No. of arrangements of paintings on the wall = 120 Answer: D. 120 arrangements Question 2: Step 1: No. of unique three-digit numbers with digits {3, 4, 5} is = 3 * 2 * 1 = 6 These 6 numbers will have 6 / 3 = 2 times 3 as hundreds digit, 2 times 4 as hundreds digit and 2 times 5 as hundreds digit. The same with tens and unit digits. Step 2: Therefore, the sum of all three-digit numbers Elmo wrote = 100 (2 * 3 + 2 * 4 + 2 * 5) + 10 (2 * 3 + 2 * 4 + 2 * 5) + (2 * 3 + 2 * 4 + 2 * 5) = (24) * (100 + 10 + 1) = 24 * 111 = 2664 Answer: E. 2 664 Question 3: Step 1: Total available seats = 6 No. of friends needs to be seated = 5 So, 1st friend has 6 options, 2nd friend has 5 options left, 3rd friend has 4 options, 4th friend has 3 options and 5th friend has 2 options. Step 2: No. of ways 5 friends can sit on 6 seats = 6 * 5 * 4 * 3 * 2 = 720 Answer: D. 720 ways ©Scholarly 2025. All rights reserved. All digital content and materials provided are proprietary and protected under copyright law. Any reproduction or sharing of digital files, including screenshots, recordings, or downloads, is strictly prohibited without the prior written consent of Scholarly. 1
Question 4: Step 1: Total no. of flags = 4 A signal can be made using 3 flags. There are 4 options to choose the 1st flag, 3 options to choose the 2nd flag and 2 options to choose the 3rd flag. Step 2: No. of unique signals can be made using four different flags = 4 * 3 * 2 = 24 Answer: D. 24 signals Question 5: Step 1: The first and last digit of 7-digit no. is fixed by 1 and 2 respectively, and for the other 5 digits we have numbers 3, 4, 5, 6 & 7. Since the no. should be unique, 2nd digit has 5 options, 3rd digit has 4 options, 4th digit has 3 options, 5th digit has 2 options and 6th digit has 1 option. Step 2: No. of 7 different digit numbers can be formed = 1 * 5 * 4 * 3 * 2 * 1 * 1 = 120 Answer: B. 120 numbers Question 6: Step 1: At Chef Alfredo’s restaurant, a customer has options to choose one each from 2 appetizers, 3 main courses, 5 desserts. Step 2: No. Of different set of meals, the restaurant could serve = 2 * 3 * 5 = 30 Answer: B. 30 sets ©Scholarly 2025. All rights reserved. All digital content and materials provided are proprietary and protected under copyright law. Any reproduction or sharing of digital files, including screenshots, recordings, or downloads, is strictly prohibited without the prior written consent of Scholarly. 2
Question 7: Step 1: Blossom, Bubbles and Buttercup are going for school dance with Huey, Dewey, and Louie. The 1st girl has 3 options, the 2nd girl has 2 options, and the 3rd girl has 1 option. Step 2: No. of ways three girls can go for dance with three boys = 3 * 2 * 1 = 6 ways Answer: D. 6 ways Question 8: Step 1: We are arranging 3 different letters. Step 2: Number of arrangements = 3! = 3 × 2 × 1 = 6 So, the ways are: ABC, ACB, BAC, BCA, CAB, CBA Answer: D. 6 Question 9: Step 1: To arrange letters in word CLUB, the 1st letter has 4 options, 2nd letter has 3 options, 3rd letter has 2 options and 4th letter has 1 option. Step 2: No. of ways the letters in word CLUB can be arranged = 4 * 3 * 2 * 1 = 24 ways Answer: E. 24 ways Question 10: SNACK DRINK Burger Hotdog Pancake Sandwich Waffle Coffee Juice Soda Tea Water ©Scholarly 2025. All rights reserved. All digital content and materials provided are proprietary and protected under copyright law. Any reproduction or sharing of digital files, including screenshots, recordings, or downloads, is strictly prohibited without the prior written consent of Scholarly. 3
Step 1: Miss Piggy wants to pick 2 snacks and 2 drinks. No. of ways she can choose 2 snacks from 5 options = (5 * 4)/2 = 10 ways No. of ways she can choose 2 drinks from 5 options = (5 * 4)/2 = 10 ways Step 2: No. of different ways Miss Piggy can pick = 10 * 10 = 100 ways Answer: D. 100 ways Question 11: Step 1: First letter: 3 choices (P, Q, or R) Second letter: 2 remaining choices Step 2: So, number of codes = 3 × 2 = 6 Codes: PQ, PR, QP, QR, RP, RQ Answer: E. 6 Question 12: Step 1: Archie plans to visit Sydney, Melbourne and Brisbane. To visit each city once, on the first visit he can choose to visit from 3 cities, on the 2nd visit he has 2 options left, on the 3rd visit he has 1 option left. Step 2: No. of different orders he can visit the 3 cities = 3 * 2 * 1 = 6 ways Answer: B. 6 ways Question 13: Step 1: To create a distinct taco, one option from each category must be chosen. Multiply the no. of options from each category = 3 types of taco shells * 4 types of meat * 3 types of cheese * 5 types of salsa. Step 2: Therefore, the no. of distinct tacos can be ordered = 3 * 4 * 3 * 5 = 180 ©Scholarly 2025. All rights reserved. All digital content and materials provided are proprietary and protected under copyright law. Any reproduction or sharing of digital files, including screenshots, recordings, or downloads, is strictly prohibited without the prior written consent of Scholarly. 4